#
ArcStereoNet: A New ArcGIS^{®} Toolbox for Projection and Analysis of Meso- and Micro-Structural Data

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## Abstract

**:**

^{®}based toolbox for stereographic projections that we implement here using Python 2.7 programming language. The reason to develop another stereographic projection package arises from the recent use of Python as an exclusive programming language within the ArcGIS

^{®}environment. This permits a more flexible approach for the development of tools with very intuitive GUIs, and also allows the user to take full advantage of all potential GIS mapping processes. The core of this new projections toolbox is based on the capability to easily apply and compare most of the commonly used statistical methods for cluster and girdle analysis of structural data. In addition to the well-known Fisher, K-means, and Bingham data elaborations, a completely new algorithm for cluster analysis and mean vector extraction (Mean Extractor from Azimuthal Data), was developed, thereby allowing a more reliable interpretation of any possible structural data distribution. Furthermore, as in any other GIS platform, users can always precisely correlate each single projected data point with the corresponding geographical/locality position, thereby merging or subdividing groups of structural stations with a simple selection procedure. ArcStereoNet also creates rose diagrams, which may be applied not only to fault/joint planes orientation data, but also for the analysis of 2D microstructural fabric parameters. These include geometrical datasets derived from the minimum bounding approach as applied to vectorized grains in thin sections. Finally, several customization settings ensure high-quality graphic outputs of plots, that also allow easy vector graphics post-processing.

## 1. Introduction

^{®}by Rocscience Inc. Some of these programmes include a huge number of useful tools, such as those for statistical analysis, for rotation and transformation functions, as well as for kinematic analysis or stress field orientation analysis. However, most programmes, with the exception of Orient, do not include geospatial analysis features and cannot, therefore, effectively link the orientation data with its corresponding spatial information and geological database. Over the years, several authors have tried to solve this problem by designing stereoplots software or ‘add-ins’ to specifically exploit the geospatial analysis functionalities running on well-known GIS platforms such as ArcGIS

^{®}or QGIS

^{®}. Unlike ArcGIS

^{®}, QGIS

^{®}is distributed with an open source license, therefore, plugins development and sharing within the users’ community is highly encouraged. Thus, a lot of examples of structural geology and orientation data analysis plugins for QGIS

^{®}can be found and downloaded online. Some of the best-known plugins include qgSurf [22] and GeoTrace [23], both coded in Python.

^{®}environment, Knox-Robinson and Gardoll [17] were the first to implement a stereonet plotting functionality for ArcView 3.0 GIS (an ESRI predecessor of modern ArcMap

^{®}), thus, becoming the forerunners of such types of tools. With the development of ArcMap

^{®}, compatible toolbars and further add-ins were designed such as the Export Toolbox [24], written in Visual Basic for Applications (VBA), that integrated a spatial averaging routine in ArcMap

^{®}8.2. The more recent OATools [25] is an ArcMap

^{®}add-in (for versions 10.2 and 10.3), always written in Visual Basic.NET (VB.NET) using Microsoft Visual Studio (2010) with ArcObjects, a developer kit for ArcGIS

^{®}for the definition of the Graphical User Interface (GUI). This last add-in combines GIS functionalities with orientation and statistical analysis such as the creation of density distribution diagrams and the calculation of mean vectors and fold axes.

^{®}(versions 10.1+), that merges the main ArcGIS

^{®}features with the semi-automatic realisation of stereoplots. It takes as input the orientation data (linear and planar features in table format) imported or created inside ArcMap

^{®}, taking advantage of its built-in functionalities of data storage and managing. In such a way, the users can at any time, within their GIS project, precisely visualise the plotted data together with the corresponding geographical/locality position. The main ASN features also include the extrapolation of statistical parameters, the application of density contour functions and the creation of rose diagrams. Moreover, the toolbox encompasses a considerable number of plot personalisation parameters that ensure high-quality publication-ready graphics, or that can be further modified with image editing software, thanks to the supported vector image output formats.

^{®}itself, ASN avoids the use of several software packages when working with oriented georeferenced data. We provide a comparison between such statistical analyses by taking a field structural dataset from folds exposed in the Macduff area of NE Scotland as a case study. In this work, we also show how ArcMap

^{®}equipped with ASN can be a valuable instrument for the simultaneous study of structural oriented data from mesoscale to microscale, using the geo and petro-structural data collected within the Palmi Shear Zone [4,26] as a practical operative example.

## 2. Methods

^{®}takes advantage of a Python 2.7.x version, installed with the software itself, to access and manipulate geo-databases and automatize various internal processes. Expert users can run Python commands directly from the Python console. Nonetheless, ArcGIS

^{®}provides various ‘ready-to-run’ toolboxes, that can also be chained together with custom Python scripts in order to realise personalised executables (i.e., Model Builder) [2,27,28,29]. In a recent addition, ArcGIS

^{®}allows coding of fully customised toolboxes, namely ‘Python-toolboxes’, by means of the arcpy library.

^{®}-supported GUI; users that habitually utilise ArcGIS

^{®}toolboxes will notice that the GUI is very similar to that of any other ArcGIS

^{®}tool.

^{®}as an ESRI shapefile, ASN can carry out stereonet- (‘Stereoplots’ tool) or rose diagram- plotting (‘Rose Diagrams’ tool) of selected records, stored within the corresponding attribute table (Figure 1). The ‘Graph to Hyperlink’ tool is useful to connect the realised plots with the geographic position of the plotted data, via hyperlink.

- Azimuth—here, azimuthal values (i.e., direction, dip direction, or trend) are stored as numeric values.
- Dip Angle or Dip_Angle—here, inclination values (i.e., dip or plunge) are stored as numeric values.
- Method—here, the data format must be specified as text values, choosing from ‘RHR’, ‘DD,’ and ‘TP’ (must be written in uppercase), indicating, respectively, the following conventional sampling methods: RHR—Right Hand Rule, DD—Dip Direction/Dip, and TP—Trend-Plunge. ASN can plot together RHR and DD data, calculating the following azimuth conversion equation:$$\mathrm{RHR}=\left(\mathrm{DD}-90\right)\mathrm{mod}360,$$
- Type—Here, the user should indicate the feature type as text values (e.g., ‘Main Foliation’, ‘Stretching Lineation’, ‘Axial Plane’ etc.). Such information is not mandatory, though highly recommended. It is functional for the legend labels but also guides the toolbox to a correct grouping and graphical representation of the different types of data. When differences between facing directions of orientation data need to be highlighted (e.g., beddings with distinguishing between normal and overturned positions), this field can be populated with distinct entries (e.g., ‘Bedding normal’ and ‘Bedding overturned’), thus, prompting the tool to treat such data separately.

^{®}, and then open the ASN toolbox and choose the desired tool (see Figure 1c). If users do not operate any data selection, the whole dataset will be considered.

#### 2.1. Azimuthal Projections

^{®}multivalue input system, consisting of a drop-down menu and a table-like box below, is called ‘Value Table’.

#### 2.1.1. ‘Stereoplots’ Tool Algorithms

- Pre-clustering. In this subprocess the azimuth frequencies are calculated, then normalized in relation to their maximum value, and finally the azimuth-dip couples are sorted by normalized azimuth frequency.
- Clustering. This an iterative subprocess, where the sorted azimuth-dip couples are analysed multiple times in order to group them together. With azimuth and dip values of the first couple representing the starting median values, each couple is compared with them and, if they do not diverge by more than a threshold value, they are grouped together and the median values are consequently refreshed. This is computed as:$$\left|\mathrm{sin}{\mathsf{\alpha}}_{\mathrm{i}}-\mathrm{sin}{\mathsf{\alpha}}^{*}\right|\le {\mathrm{t}}_{1};$$$$\left|\mathrm{cos}{\mathsf{\alpha}}_{\mathrm{i}}-\mathrm{cos}{\mathsf{\alpha}}^{*}\right|\le {\mathrm{t}}_{1};$$$$\left|\mathrm{sin}{\mathsf{\delta}}_{\mathrm{i}}-\mathrm{sin}{\mathsf{\delta}}^{*}\right|\le {\mathrm{t}}_{2};$$
_{i}and δ_{i}are the azimuth and dip values of the i-th couple, while α* and δ* are the current azimuth and dip median values, respectively. Both the sine and the cosine differences (Equations (2) and (3)) are needed for azimuth values, because a numerical value ranging from 0 to 360 can be unequivocally expressed only by considering both its sine and cosine contemporaneously. Instead, as the dip value ranges between 0 and 90, just one of its sine and cosine values is sufficient (Equation (4)). The maximum value for the azimuth threshold (t_{1}) is 2, while for the inclination threshold (t_{2}) it is 1, as the sine function ranges between −1 and 1 for azimuth values and between 0 and 1 for the dip values. The clustering subprocess is reiterated until no more clusters can be extracted; the remaining couples, if present, are considered as spurious. An important role here is covered by the azimuth and inclination tolerances set by the user through the corresponding Value Table parameters (Figure 3c), as the thresholds (t_{1}and t_{2}) are proportional to such values. Experimental tests show that even a small variation of tolerance values can sometimes determine significant variations on the result. It is possible for the users to quickly test different tolerance values multiple times, by unchecking the ‘Store Image Output’ option (Figure 2d). In this way, they can obtain the graphical result that best suits their needs and preferences without wasting memory space. Another useful option to check is the ‘Track M.E.A.D. Behaviour’ (Figure 3d), which plots the clustered data (poles or lines) with different symbols (e.g., symbol ‘1′ for data that falls into the first cluster, ‘2′ for second cluster, no symbol for spurious data, etc.). This can be helpful to understand the actual influence of the user-controlled parameters on the clustering process and to simplify their setup (Figure 5). - Post-clustering. This subprocess performs a post-filtering operation, double-checking all extracted families and returning as output only the number of clusters required by the user, selecting the most populated ones. If such a number is higher than the actual number of families extracted by the clustering process, the function will return all the obtained clusters.

_{i}represents the i-th azimuth value, expressed in radians, within the n-elements cluster and θ is the mean angle expressed in degrees. The inclination average value, instead, is calculated by applying the arithmetic mean formula, as the inclination values range from 0 to 90 and do not ‘wrap-around’. This computation is applied for each cluster obtained by the clustering process.

#### 2.2. Rose Diagrams

#### ‘Rose Diagrams’ Tool Algorithms

_{i}is the i-th azimuth value within the n-elements cluster. Here, R is the mean resultant length (ranging between 0 and 1), and its value determines the length of the arrow representing the mean vector on the plot. If the ‘Mirrored Behaviour’ option is selected, the supplementary mean azimuth direction (θ’) is also computed for each cluster and R is represented on the plot as a double-headed arrow, pointing towards both mean vectors directions. If the user prompts for a weighted rose diagram, the magnitude of the selected weights must be evaluated within the calculation of the mean vectors. Therefore, Equations (5) and (6) become, respectively:

_{i}representing the i-th weight value associated to each azimuth value (α

_{i}) within the n-elements cluster.

#### 2.3. Output Images

^{®}default scratch folder and automatically open it with the default local image viewer. If the user also requires the log file, it will be saved as a temporary file and automatically opened too. These files will be deleted by ASN immediately after the user prompts for a new temporary image.

## 3. ASN Worked Examples

#### 3.1. Macduff Case Study: Algorithms Comparison

#### 3.2. Palmi Shear Zone Case Study: Mesostructural and Microstructural Data Comparison

#### 3.2.1. Mesostructural Data Analysis

#### 3.2.2. Microstructural Data Analysis

^{®}platform, is suitable as an ‘ASN-friendly’ input feature. The 2D orientation data, obtained via Min-GSD through a stepwise controlled overlaying procedure of X-Ray and Grain-boundary maps of thin sections, permitted storage of microstructural information of minerals in shapefile format [47] (Figure 17a and Figure 18a), and is provided in Table S3 and Table S4 within Supplementary Materials. Specifically, the minimum bounding geometry approach was applied to about 800 clasts per thin section, with the azimuthal values of the preferred orientation of porphyroclasts ranging from 0 to 180 degrees with respect to the normal axis to the main foliation of the sample (Figure 17b). These values can be computed by the ‘Rose Diagrams’ tool while the feature type input parameter can be filled with the mineral name field. Six and twelve rose diagrams have been created, respectively, for PAL11 and PAL12a samples. In both samples, we constructed standard rose diagrams (Figure 17c,e,g, and Figure 18b,d,f,h,j,l), which display directional data and the frequency of minerals, and also weighted rose diagrams (Figure 17b,f,h, and Figure 18c,e,g,i,k,m), which were useful to assign greater or smaller importance to each grain orientation as a function of a specific weighting factor (e.g., their area in mm

^{2}). In both cases, we selected the ‘Mirrored behaviour’ option as the azimuthal values only range from 0 to 180 degrees.

## 4. Discussions

^{®}features with the semi-automatic creation of stereoplots, and is compatible with the latest versions of ArcMap

^{®}(versions 10.3+).

^{®}platform, rather than other GIS software, arises from the fact that, starting from the 10.1 version, it is possible to create various personalised Python toolboxes (i.e., that can use several open access Python libraries). These can be linked together with other existing tools (i.e., Model Builder [2,28,29,47]) within a very user-friendly ArcGIS

^{®}-like GUI. Furthermore, since the Python version attached to ArcGIS

^{®}differs according to ArcGIS

^{®}version itself, then the ASN code is able to recognize it and consequently adapt the automatic download and installation routine of the suitable libraries. This extends its compatibility from ArcGIS

^{®}10.3 to the latest distribution (see Supplementary Material—S5).

^{®}supported GUI for non-Python users. Moreover, ASN allows the user to easily compare several types of analytical statistical methods, including, for the first time, a totally new clustering and mean vector extracting algorithm (Mean Extractor from Azimuthal Data). The M.E.A.D. clustering process takes as input the orientation data, expressed as a list of azimuth-dip couples (i.e., strike-dip for planar features or trend-plunge for linear features), and groups it into a user-defined number of families (i.e., the ‘Number of Clusters’ parameter). The degree of tolerance is driven by two user-controlled percentage values, allowing, in turn, a more incisive analytical choice (see Figure 4). The tool also helps the user in setting the algorithm-control parameters, by providing the possibility to track the behaviour of the M.E.A.D. clustering process (Figure 3d and Figure 5).

^{®}, other toolbars and add-ins were designed, such as the Export Toolbox [24], written in VBA, that provided methods to export oriented data managed in ArcMap

^{®}8.2 to 3D geoscientific modelling tools (i.e., Editeur Géologique, developed by BRGM, and GOCAD

^{®}[50]) and also integrated a spatial averaging routine within ArcMap

^{®}itself. These tools are obviously out-dated and no longer compatible with recent versions of ArcGIS

^{®}which in the meantime has evolved towards more open data sharing modes and scripting methods.

^{®}environment is OATools [25], an add-in for ArcMap

^{®}10.2 and 10.3 versions, written in Visual Basic.NET (VB.NET). This takes advantage of GIS functionalities to carry out the spatial analysis of structural data. Its main features include azimuthal projection of oriented data, extraction of mean vector and fold axes, creation of density distribution diagrams, creation of rose histograms, and mapping of spatial averages.

^{®}tool for the analysis of 3D and 2D oriented datasets. As a result, it smoothly blends with other built-in ArcGIS

^{®}toolboxes and its functionalities could be considerably expanded or enhanced thanks to the huge amount of available open access Python libraries. Python-toolboxes are in fact the ESRI suggested approach for creating Python-based tools since ArcGIS

^{®}10.1 version. Moreover, ASN brings in the possibility of choosing between several methods to carry out clustering analysis (for the first time applicable also to rose diagrams) and mean vector extraction, as well as various density distribution functions, thereby providing the user a wide range of statistical analysis techniques to apply to oriented data.

## 5. Conclusions

^{®}Python-toolbox for azimuthal projections useful for 2D and 3D oriented data analysis. It encourages greater user awareness via a stepwise guided control of the different analytical techniques used for 3D and 2D data projections in a GIS environment.

- A totally new clustering and mean-vector extracting algorithm used to obtain size-decreasing ordered clusters (i.e., M.E.A.D), and which enables a greater background noise control through tolerance parameters.
- The capability of analysing both cluster and girdle-like distribution patterns with several algorithms.
- The capability of contemporaneously running multiple data analysis algorithms to extract statistical parameters.
- The capability of storing applied algorithm results on automatically compiled log files.
- The capability of testing several parameter settings at a time via the use of temporary images that do not waste disk memory.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Macduff dataset without any data differentiation evidenced by the field investigator (i.e., all data is labelled as generic ‘Fold limb’).

ID | Azimuth | Dip_Angle | Method | Type |
---|---|---|---|---|

0 | 206 | 65 | RHR | Fold limb |

1 | 212 | 25 | RHR | Fold limb |

2 | 217 | 40 | RHR | Fold limb |

3 | 197 | 24 | RHR | Fold limb |

4 | 192 | 20 | RHR | Fold limb |

5 | 213 | 40 | RHR | Fold limb |

6 | 206 | 74 | RHR | Fold limb |

7 | 205 | 68 | RHR | Fold limb |

8 | 190 | 35 | RHR | Fold limb |

9 | 212 | 35 | RHR | Fold limb |

10 | 203 | 85 | RHR | Fold limb |

11 | 205 | 52 | RHR | Fold limb |

12 | 210 | 55 | RHR | Fold limb |

13 | 204 | 48 | RHR | Fold limb |

14 | 206 | 70 | RHR | Fold limb |

15 | 212 | 83 | RHR | Fold limb |

16 | 215 | 84 | RHR | Fold limb |

17 | 210 | 77 | RHR | Fold limb |

18 | 214 | 81 | RHR | Fold limb |

19 | 207 | 80 | RHR | Fold limb |

20 | 205 | 81 | RHR | Fold limb |

21 | 207 | 86 | RHR | Fold limb |

22 | 206 | 85 | RHR | Fold limb |

23 | 214 | 63 | RHR | Fold limb |

24 | 30 | 65 | RHR | Fold limb |

25 | 45 | 70 | RHR | Fold limb |

26 | 27 | 75 | RHR | Fold limb |

27 | 33 | 83 | RHR | Fold limb |

28 | 33 | 74 | RHR | Fold limb |

29 | 40 | 70 | RHR | Fold limb |

30 | 15 | 65 | RHR | Fold limb |

31 | 34 | 76 | RHR | Fold limb |

32 | 32 | 75 | RHR | Fold limb |

33 | 32 | 88 | RHR | Fold limb |

34 | 34 | 80 | RHR | Fold limb |

35 | 35 | 80 | RHR | Fold limb |

36 | 32 | 70 | RHR | Fold limb |

37 | 15 | 85 | RHR | Fold limb |

38 | 24 | 72 | RHR | Fold limb |

39 | 25 | 70 | RHR | Fold limb |

**Table A2.**Macduff dataset with data differentiation evidenced by the field investigator (i.e., data is split into ‘West limb of Anticlines’ and ‘East limb of Anticlines’).

ID | Azimuth | Dip_Angle | Method | Type |
---|---|---|---|---|

0 | 206 | 65 | RHR | West limb of Anticlines |

1 | 212 | 25 | RHR | West limb of Anticlines |

2 | 217 | 40 | RHR | West limb of Anticlines |

3 | 197 | 24 | RHR | West limb of Anticlines |

4 | 192 | 20 | RHR | West limb of Anticlines |

5 | 213 | 40 | RHR | West limb of Anticlines |

6 | 206 | 74 | RHR | West limb of Anticlines |

7 | 205 | 68 | RHR | West limb of Anticlines |

8 | 190 | 35 | RHR | West limb of Anticlines |

9 | 212 | 35 | RHR | West limb of Anticlines |

10 | 203 | 85 | RHR | West limb of Anticlines |

11 | 205 | 52 | RHR | West limb of Anticlines |

12 | 210 | 55 | RHR | West limb of Anticlines |

13 | 204 | 48 | RHR | West limb of Anticlines |

14 | 206 | 70 | RHR | West limb of Anticlines |

15 | 212 | 83 | RHR | East limb of Anticlines |

16 | 215 | 84 | RHR | East limb of Anticlines |

17 | 210 | 77 | RHR | East limb of Anticlines |

18 | 214 | 81 | RHR | East limb of Anticlines |

19 | 207 | 80 | RHR | East limb of Anticlines |

20 | 205 | 81 | RHR | East limb of Anticlines |

21 | 207 | 86 | RHR | East limb of Anticlines |

22 | 206 | 85 | RHR | East limb of Anticlines |

23 | 214 | 63 | RHR | East limb of Anticlines |

24 | 30 | 65 | RHR | East limb of Anticlines |

25 | 45 | 70 | RHR | East limb of Anticlines |

26 | 27 | 75 | RHR | East limb of Anticlines |

27 | 33 | 83 | RHR | East limb of Anticlines |

28 | 33 | 74 | RHR | East limb of Anticlines |

29 | 40 | 70 | RHR | East limb of Anticlines |

30 | 15 | 65 | RHR | East limb of Anticlines |

31 | 34 | 76 | RHR | East limb of Anticlines |

32 | 32 | 75 | RHR | East limb of Anticlines |

33 | 32 | 88 | RHR | East limb of Anticlines |

34 | 34 | 80 | RHR | East limb of Anticlines |

35 | 35 | 80 | RHR | East limb of Anticlines |

36 | 32 | 70 | RHR | East limb of Anticlines |

37 | 15 | 85 | RHR | East limb of Anticlines |

38 | 24 | 72 | RHR | East limb of Anticlines |

39 | 25 | 70 | RHR | East limb of Anticlines |

## Appendix B

REEF 1 | |

Main Foliation = 112 | |

Stretching Lineation = 10 | |

CONTOUR INFO | |

Applied on -> | Main Foliation |

Method -> | Kamb (linear smoothing) |

St.Dev. -> | 1.5 |

STATISTICS | |

Main Foliation [K-means mean(s)] -> | 311/74 |

Main Foliation [M.E.A.D. + Fisher mean(s)] -> | 316/69 |

Main Foliation [Fisher Stats]: | |

- R value (length of the mean vector) -> | 0.924 |

- Fisher angle (confidence radius) -> | 4.62 deg |

- K value (dispersion factor) -> | 13.02 |

Stretching Lineation [Bingham best fit plane] -> | 320/66 |

Note that mean values are expressed as follows: | |

- strike/dip (planar features) | |

- trend/plunge (linear features) | |

Log file automatically compiled by ArcStereoNet |

REEF 2 | ||||

Main Foliation = 34 | ||||

Stretching Lineation = 19 | ||||

CONTOUR INFO | ||||

Applied on -> | Main Foliation | |||

Method -> | Kamb (linear smoothing) | |||

St.Dev. -> | 1.5 | |||

STATISTICS | ||||

Main Foliation [K-means mean(s)] -> | 036/60 | 090/68 | 139/72 | 275/74 |

Main Foliation [M.E.A.D. + Fisher mean(s)] -> | 098/67 | 275/74 | 036/61 | 144/72 |

Main Foliation [Fisher Stats]: | ||||

- R value (length of the mean vector) -> | 0.941 | 0.966 | 0.963 | 0.996 |

- Fisher angle (confidence radius) -> | 10.30 deg | 9.06 deg | 16.93 deg | 10.04 deg |

- K value (dispersion factor) -> | 15.87 | 26.36 | 21.38 | 151.70 |

Stretching Lineation [K-means mean(s)] -> | 116/05 | |||

Note that mean values are expressed as follows: | ||||

- strike/dip (planar features) | ||||

- trend/plunge (linear features) | ||||

Log file automatically compiled by ArcStereoNet |

BEACH | ||||

Main Foliation = 275 | ||||

Stretching Lineation = 56 | ||||

CONTOUR INFO | ||||

Applied on -> | Main Foliation | |||

Method -> | Kamb (linear smoothing) | |||

St.Dev. -> | 1.5 | |||

STATISTICS | ||||

Main Foliation [M.E.A.D. + Fisher mean(s)] -> | 101/69 | 283/70 | 064/67 | 257/77 |

Main Foliation [Fisher Stats]: | ||||

- R value (length of the mean vector) -> | 0.967 | 0.969 | 0.969 | 0.994 |

- Fisher angle (confidence radius) -> | 2.22 deg | 4.09 deg | 4.52 deg | 3.22 deg |

- K value (dispersion factor) -> | 30.16 | 31.55 | 31.55 | 153.40 |

Stretching Lineation [K-means mean(s)] -> | 099/04 | |||

Note that mean values are expressed as follows: | ||||

- strike/dip (planar features) | ||||

- trend/plunge (linear features) | ||||

Log file automatically compiled by ArcStereoNet |

MALOPASSO | |

Main Foliation = 39 | |

Stretching Lineation = 8 | |

CONTOUR INFO | |

Applied on -> | Main Foliation |

Method -> | Kamb (linear smoothing) |

St.Dev. -> | 1.5 |

STATISTICS | |

Main Foliation [M.E.A.D. + Fisher mean(s)] -> | 310/69 |

Main Foliation [Fisher Stats]: | |

- R value (length of the mean vector) -> | 0.957 |

- Fisher angle (confidence radius) -> | 5.28 deg |

- K value (dispersion factor) -> | 22.69 |

Stretching Lineation [M.E.A.D. + Fisher mean(s)] -> | 127/10 |

Stretching Lineation [Fisher Stats]: | |

- R value (length of the mean vector) -> | 0.980 |

- Fisher angle (confidence radius) -> | 9.29 deg |

- K value (dispersion factor) -> | 43.19 |

Note that mean values are expressed as follows: | |

- strike/dip (planar features) | |

- trend/plunge (linear features) | |

Log file automatically compiled by ArcStereoNet |

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**Figure 1.**Example of ArcMap

^{®}(version 10.6.1) equipped with ArcStereoNet. After creating a shapefile storing oriented data (

**a**) and selecting the records stored inside its attribute table (

**b**), the user can open the ArcStereoNet toolbox (

**c**) from the ArcToolbox window and choose the preferred tool.

**Figure 2.**‘Stereoplots’ tool layout. Green dots indicate required parameters. (

**a**) Oriented dataset input; requires a shapefile (point, line, and polygon features types are supported). (

**b**) Azimuth, Dip Angle, Method, and Type fields inputs, selectable through the drop-down menus. (

**c**) Plotting data Value Table; for each added feature type the user can specify the plotting colour, pole, or vector symbol and size, cyclographic trace style, and width. (

**d**) Output image settings; the stereoplot can be saved as a temporary file by unchecking the ‘Store Image Output’ option, otherwise an output file path can be selected. (

**e**) ‘Contour & Statistics’ submenu; see Figure 3 for details. (

**f**) Plot customisation submenu; enables the look of stereoplot to be customised. (

**g**) Plotting options submenu; the stereonet type can be chosen (equal-area or equal-angle) and the ‘Write Log File’ option can be checked to prompt the tool to compile a text file storing statistical information concerning the plotted data.

**Figure 3.**Expanded ‘Contour & Statistics’ submenu of ‘Stereoplots’ tool. (

**a**) ‘Apply Contour’ Value Table; the user can choose the preferred contour density function under the ‘Method’ column, and set other parameters such as standard deviation, style, colour, and transparency. (

**b**) Show a colour bar referred to the applied contour. (

**c**) ‘Extract Mean Vectors’ Value Table; the algorithm-control parameters are ‘Algorithm’, to choose the preferred algorithm, ‘Number of Clusters’, Azimuth and Inclination tolerances and ‘Fisher confidence’. The other parameters gather settings for graphic appearance. (

**d**) Track Mean Extractor from Azimuthal Data (M.E.A.D.) clustering behaviour option will only apply on clusters extracted by mean of the M.E.A.D. clustering process (see “‘Stereoplots’ tool algorithms” subparagraph for details).

**Figure 4.**Mean Extractor from Azimuthal Data (M.E.A.D.) algorithm flow chart. Ovals indicate input/output objects, squares indicate algorithm subprocesses. The azimuth-dip couples are first sorted by most frequent azimuth value (pre-clustering); then the clustering subprocess is applied, taking care of the user-controlled tolerance parameters. The raw output is then refined in a post-clustering phase and the required number of clusters is returned. Finally, these are fed into the mean vector extracting process that outputs the final result, consisting of one or more mean vectors.

**Figure 5.**Influence of azimuth and inclination tolerance parameters on the M.E.A.D. clustering process, highlighted with ‘Track M.E.A.D. behaviour’ option (Figure 3d). (

**a**) Two-clusters model with an azimuth tolerance of 20% and an inclination tolerance of 30%. Almost all plotted data is grouped into two different clusters (1 and 2). (

**b**) Two-clusters model with an azimuth tolerance of 13% and an inclination tolerance of 10%. Extracted clusters tend to be less dispersed and, consequently, much more data is evaluated as spurious (i.e., not gathered within any cluster).

**Figure 6.**‘Rose Diagrams’ tool layout. Green dots indicate required parameters. (

**a**) Oriented dataset input; requires a shapefile (point, line, and polygon features types are supported). (

**b**) Azimuth and Type fields inputs, selectable through the drop-down menus. (

**c**) Plotting data Value Table; for each added feature type, the user can specify the bar colour and whether to show the mean vectors or not, with a determined number of clusters and azimuth tolerance. (

**d**) Output image settings; the rose diagram can be saved as a temporary file by unchecking the ‘Store Image Output’ option, otherwise an output file path can be selected. (

**e**) Plot customisation submenu; rose diagram look can be here customised. (

**f**) Plotting options submenu; ‘Mirrored behaviour’ option allows to prompt for a specular rose diagram, ‘Weighted Rose Diagram’ option allows the user to weight data (a weight field must be provided). The ‘Write Log File’ option can be checked to prompt the tool to compile a text file storing statistical information concerning the plotted data.

**Figure 7.**Graph To Hyperlink tool. (

**a**) Tool layout; one or multiple raster images are required as input. Such images are meant to be stereoplots or rose diagrams realised by the ASN related tools. An output feature class is also required; here, the spatial information and the hyperlinks to each image is stored. (

**b**) Example of Graph To Hyperlink result. Green circles indicate four different sampling stations; the corresponding plots pop out from each of them.

**Figure 8.**Field photograph of a NNE-trending upright synform that folds bedding (highlighted in yellow) and develops a broadly axial-planar cleavage (in green). (Macduff area: UK Grid: NJ7190 6465).

**Figure 9.**Application of ArcStereoNet algorithms with default control parameters for the extraction of mean vectors from the Macduff area dataset, treated as a single feature type. (

**a**) ASN graphic result; (

**b**) portion of Macduff dataset attribute table, with all records sharing the same feature type (i.e., “Fold limb”); (

**c**) ASN log file showing algorithm statistics and results; and (

**d**) “Extract Mean Vector” Value Table showing the algorithm settings.

**Figure 10.**Application of ArcStereoNet algorithms with customised control parameters for the extraction of mean vectors from the Macduff area dataset, treated as a single feature type. (

**a**) ASN graphic result; (

**b**) portion of Macduff dataset attribute table, with all records sharing the same feature type (i.e., ‘Fold limb’); (

**c**) ASN log file showing algorithm statistics and results; and (

**d**) ‘Extract Mean Vector’ Value Table showing the algorithm settings.

**Figure 11.**Application of ArcStereoNet algorithms with customised control parameters for the extraction of mean vectors from the Macduff area dataset, grouped in two different feature types. (

**a**) ASN graphic result; (

**b**) portion of Macduff dataset attribute table, with records displaying two different feature types (i.e., ‘East limb of Anticlines’ and ‘West limb of Anticlines’); (

**c**) ASN log file showing algorithm statistics and results; and (

**d**) ‘Extract Mean Vector’ Value Table showing the algorithm settings.

**Figure 12.**Geological background of the Palmi Shear Zone: (

**a**) Geological map of the Calabrian metamorphic complexes (after Angì et al. [46]); (

**b**) Geological Map of the case study area of the Palmi Shear zone with trends of the main foliations and average stretching lineations, (white circles represent location of each structural station, while red circles represent sample locations).

**Figure 13.**‘Reef 1′ station: (

**a**) equal-area azimuthal projection and statistical analysis of main foliations and stretching lineations data and (

**b**) field example of isoclinally folded foliation in mylonites (tonalites interlayered with paragneisses). The ASN log file is provided in Appendix B (Table A3).

**Figure 14.**‘Reef 2′ station: (

**a**) equal-area azimuthal projection and statistical analysis of main foliations and stretching lineation data and (

**b**) field example of mylonitic foliation subparallel to fold axial surface in tonalites. The ASN log file is provided in Appendix B (Table A4).

**Figure 15.**‘Beach’ station: (

**a**) equal-area azimuthal projection and statistical analysis of main foliations and stretching lineation data and (

**b**) field example of W–E oriented mylonitic foliation developed in tonalites interlayered with paragneisses. The ASN log file is provided in Appendix B (Table A5).

**Figure 16.**‘Malopasso’ station: (

**a**) equal-area azimuthal projection and statistical analysis of main foliations and stretching lineation data and (

**b**) field example of tight isoclinal folds and smaller sheath folds developed in calc-silicates and skarns. The ASN log file is provided in Appendix B (Table A6).

**Figure 17.**Application of ‘Rose Diagrams’ tool to PAL11 microstructural data. (

**a**) Porphyroclast grain boundary detection map obtained via Min-GSD routine [4]; (

**b**) scheme of the minimum bounding geometry data extraction for each single clast, where α represents the angle between the normal to the main foliation in thin section with the major axis of the bounding box; (

**c**,

**e**,

**g**) unweighted rose diagrams; (

**d**,

**f**,

**h**) weighted rose diagrams based on grains cumulative area (in mm

^{2}).

**Figure 18.**Application of ‘Rose Diagrams’ tool to PAL12a microstructural data. (

**a**) Porphyroclast grain boundary detection map obtained via Min-GSD routine [4]; (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**) unweighted rose diagrams; (

**c**,

**e**,

**g**,

**i**,

**k**,

**m**) weighted rose diagrams based on grains cumulative area (in mm

^{2}).

**Table 1.**Influences of user-controlled parameters on ArcStereoNet (ASN) algorithms. An ‘X’ symbol means that the parameter (row) has an effect on the algorithm (column).

M.E.A.D. + Fisher | M.E.A.D. | K-Means | Bingham | |
---|---|---|---|---|

Number of Clusters | X | X | X | - |

M.E.A.D. Azimuth tolerance | X | X | - | - |

M.E.A.D. Inclination tolerance | X | X | - | - |

Fisher Confidence | X | - | - | - |

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## Share and Cite

**MDPI and ACS Style**

Ortolano, G.; D’Agostino, A.; Pagano, M.; Visalli, R.; Zucali, M.; Fazio, E.; Alsop, I.; Cirrincione, R.
ArcStereoNet: A New ArcGIS^{®} Toolbox for Projection and Analysis of Meso- and Micro-Structural Data. *ISPRS Int. J. Geo-Inf.* **2021**, *10*, 50.
https://doi.org/10.3390/ijgi10020050

**AMA Style**

Ortolano G, D’Agostino A, Pagano M, Visalli R, Zucali M, Fazio E, Alsop I, Cirrincione R.
ArcStereoNet: A New ArcGIS^{®} Toolbox for Projection and Analysis of Meso- and Micro-Structural Data. *ISPRS International Journal of Geo-Information*. 2021; 10(2):50.
https://doi.org/10.3390/ijgi10020050

**Chicago/Turabian Style**

Ortolano, Gaetano, Alberto D’Agostino, Mario Pagano, Roberto Visalli, Michele Zucali, Eugenio Fazio, Ian Alsop, and Rosolino Cirrincione.
2021. "ArcStereoNet: A New ArcGIS^{®} Toolbox for Projection and Analysis of Meso- and Micro-Structural Data" *ISPRS International Journal of Geo-Information* 10, no. 2: 50.
https://doi.org/10.3390/ijgi10020050